Finite Group Databasebeta

← #33085651

Subgroups — #33085651

Order 18688.

1308 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989353C211yesmaximal, characteristic
2C2×#17988635C211yesmaximal, characteristic, complemented
3#22618520C211yesmaximal, characteristic, complemented
4C2×#17988605C211yesmaximal, characteristic
5C2×#17988603C211yesmaximal, characteristic
6#22609984C218yesmaximal, complemented
7C2×#17988359C211yesmaximal, characteristic, complemented
8C2×#344×C73C211yesmaximal, characteristic, complemented
9C22×#11924028C2211yescharacteristic
10#17989353—22no—
11#17989353—22no—
12#17989353C414yescomplemented
13#17989353C414yescomplemented
14C2×#14556599C2214yes—
15C2×#14556597—22no—
16C22×#11924012C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C2×M16×D73—22no—
19C2×#14556550C2211yescharacteristic
20#17988635—22no—
21#17988635—22no—
22C2×#14556526C2214yescomplemented
23#17988630—22no—
24#17988627—22no—
25#17988623C2214yescomplemented
26#17988605—22no—
27#17988605C2214yes—
28#17988603—22no—
29#17988603C2214yes—
30C2×#14556519—22no—
31C2×#14556517—22no—
32#17988359C2214yescomplemented
33C22×M16×C73C2211yescharacteristic
34C22×M16×C73C2211yescharacteristic
35C2×#117×C73C2211yescharacteristic
36#344×C73C2214yescomplemented
37C2×#11924028—21no—
38C2×#11924028—21no—
39C2×#11924028—21no—
40C2×#11924028—21no—
41C2×#11924028—21no—
42C2×#11924028—21no—
43C2×#11924028C2×C412yes—
44C2×#11924028C2×C412yes—
45C2×#11924028D412yes—
46C2×#11924028D412yes—
47C2×#11924028Q812yes—
48C2×#11924028C2312yes—
49C22×Dic146Q811yescharacteristic
50C22×D292Q811yescharacteristic
51C22×C22⋊D73—21no—
52C22×C4×D73—21no—
53#14556599—28no—
54#14556599C2×C4116yescomplemented
55#14556597—28no—
56#14556597—28no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012—21no—
60C2×#11924012—21no—
61C2×#11924012—21no—
62C2×#11924012C2×C412yes—
63C2×#11924012C2×C412yes—
64C2×#11924012D412yes—
65C2×#11924012D412yes—
66C2×#11924012D412yes—
67C2×#11924012D412yes—
68C2×#11924012C2312yes—
69C2×#11924011—24no—
70M16×D73—28no—
71M16×D73—28no—
72C22×#10596831—21no—
73C22×#10596831C2312yes—
74C2×C8×D73—24no—
75#14556550—21no—
76#14556550—21no—
77#14556550—21no—
78#14556550C2312yes—
79C2×C4⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C4×Dic73—21no—
82#14556526—28no—
83#14556524—24no—
84#14556522—24no—
85#14556519—28no—
86#14556517—28no—
87C23×C4×C73C2311yescharacteristic
88C2×M16×C73—21no—
89C2×M16×C73—21no—
90C2×M16×C73—21no—
91C2×M16×C73—21no—
92C2×M16×C73—21no—
93C2×M16×C73—21no—
94C2×M16×C73—21no—
95C2×M16×C73—21no—
96C2×M16×C73C2×C412yes—
97C2×M16×C73C2×C412yes—
98C2×M16×C73C2312yes—
99C2×M16×C73C2312yes—
100C22×C8×C73—21no—
101C22×C8×C73—21no—
102#117×C73—21no—
103#117×C73—21no—
104#117×C73—21no—
105#117×C73C2312yes—
106C2×C4⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C42×C73—21no—
109C23×D73—21no—
110#11924028—22no—
111#11924028—22no—
112#11924028—22no—
113#11924028—22no—
114#11924028—22no—
115#11924028—22no—
116#11924028—22no—
117#11924028—22no—
118#11924028—22no—
119#11924028—22no—
120#11924028—22no—
121#11924028—22no—
122#11924028C4⋊C414yes—
123#11924028C4⋊C414yes—
124#11924028C22×C414yes—
125#11924028C2×D414yes—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146—21no—
129C2×Dic146C4⋊C412yes—
130C2×Dic146C4⋊C412yes—
131C2×Dic146C2×Q812yes—
132C2×D292—21no—
133C2×D292—21no—
134C2×D292—21no—
135C2×D292C4⋊C412yes—
136C2×D292C4⋊C412yes—
137C2×D292C2×Q812yes—
138C2×C22⋊D73—22no—
139C2×C22⋊D73—22no—
140C2×C22⋊D73—22no—
141C2×C22⋊D73—22no—
142C2×C22⋊D73—22no—
143C2×C22⋊D73—22no—
144C22×Dic73—21no—
145C22×Dic73—41no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152#11924012—22no—
153#11924012—22no—
154#11924012—41no—
155#11924012—41no—
156#11924012C22⋊C414yes—
157#11924012C22⋊C414yes—
158#11924012C22⋊C414yes—
159#11924012C22⋊C414yes—
160#11924011—216no—
161C2×#10596831—22no—
162C2×#10596831—41no—
163C2×#10596831—41no—
164C2×#10596831C22×C414yes—
165C2×#10596831C2×D414yes—
166C2×#10596831C2×D414yes—
167C8×D73—216no—
168C4⋊Dic73—22no—
169C4⋊Dic73—41no—
170C22⋊Dic73—22no—
171C22⋊Dic73—41no—
172C4×Dic73—22no—
173C4×Dic73—41no—
174C24×C73#4111yescharacteristic
175C22×C4×C73—41no—
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×Q811yescharacteristic
185C22×C4×C73C2×Q811yescharacteristic
186C22×C4×C73#4111yescharacteristic
187C22×C4×C73#4111yescharacteristic
188C22×C4×C73#4111yescharacteristic
189C22×C4×C73C2411yescharacteristic
190M16×C73—22no—
191M16×C73—22no—
192M16×C73—22no—
193M16×C73—22no—
194M16×C73—22no—
195M16×C73—41no—
196M16×C73—41no—
197M16×C73C22×C414yes—
198C2×C8×C73—22no—
199C2×C8×C73—22no—
200C2×C8×C73—22no—
201C2×C8×C73—22no—
202C2×C8×C73—41no—
203C2×C8×C73—41no—
204C4⋊C4×C73—22no—
205C4⋊C4×C73—41no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—41no—
208C42×C73—22no—
209C42×C73—41no—
210C23×C73—81no—
211C23×C73#11711yescharacteristic
212C23×C73#11711yescharacteristic
213C23×C73#12111yescharacteristic
214C23×C73#12111yescharacteristic
215C23×C73C22⋊Q811yescharacteristic
216C23×C73C22⋊Q811yescharacteristic
217C23×C73C2×#4111yescharacteristic
218C22×D73—22no—
219C22×D73—22no—
220C22×D73—22no—
221C22×D73—82no—
222C2×C4×C73—42no—
223C2×C4×C73—82no—
224C2×C4×C73C2×C22⋊C411yescharacteristic
225C2×C4×C73C2×C22⋊C411yescharacteristic
226C2×C4×C73C2×C22⋊C411yescharacteristic
227C2×C4×C73C2×C22⋊C411yescharacteristic
228C2×C4×C73C2×C4⋊C411yescharacteristic
229C2×C4×C73C2×C4⋊C411yescharacteristic
230C2×C4×C73C2×C4⋊C411yescharacteristic
231C2×C4×C73C2×C4⋊C411yescharacteristic
232C2×C4×C73#11711yescharacteristic
233C2×C4×C73#11711yescharacteristic
234C2×C4×C73#12111yescharacteristic
235C2×C4×C73#12111yescharacteristic
236C2×C4×C73#12111yescharacteristic
237C2×C4×C73#12111yescharacteristic
238C2×C4×C73#12111yescharacteristic
239C2×C4×C73#12111yescharacteristic
240C2×C4×C73C22⋊Q811yescharacteristic
241C2×C4×C73C22⋊Q811yescharacteristic
242C2×C4×C73C22⋊Q811yescharacteristic
243C2×C4×C73C22⋊Q811yescharacteristic
244C2×C4×C73C22⋊Q811yescharacteristic
245C2×C4×C73C22⋊Q811yescharacteristic
246C2×C4×C73C23×C411yescharacteristic
247C2×C4×C73C22×D411yescharacteristic
248C2×C4×C73C22×D411yescharacteristic
249C2×C4×C73C22×D411yescharacteristic
250C2×C4×C73C22×Q811yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C22⋊D73—24no—
253C22⋊D73—24no—
254C22⋊D73—24no—
255C22⋊D73—24no—
256C2×Dic73—22no—
257C2×Dic73—22no—
258C2×Dic73—22no—
259C2×Dic73—42no—
260C2×Dic73—82no—
261D292—22no—
262D292—22no—
263D292—22no—
264D292C2×C4⋊C414yes—
265C4×D73—24no—
266C4×D73—24no—
267C4×D73—24no—
268C4×D73—24no—
269Dic146—22no—
270Dic146—22no—
271Dic146—22no—
272Dic146C2×C4⋊C414yes—
273C8×C73—24no—
274C8×C73—42no—
275#10596831—42no—
276#10596831C2×C22⋊C418yes—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73#38011yescharacteristic
285C22×C73#38011yescharacteristic
286C22×C73#38011yescharacteristic
287C22×C73#38011yescharacteristic
288C22×C73C2×#11711yescharacteristic
289C22×C73C2×#12111yescharacteristic
290C22×C73C2×C22⋊Q811yescharacteristic
291C2×D73—24no—
292C2×D73—44no—
293C2×D73—82no—
294C2×D73—82no—
295C4×C73—82no—
296C4×C73#38011yescharacteristic
297C4×C73#38011yescharacteristic
298C4×C73#38011yescharacteristic
299C4×C73#38011yescharacteristic
300C4×C73C22×C22⋊C411yescharacteristic
301C4×C73C22×C4⋊C411yescharacteristic
302C4×C73C2×#12111yescharacteristic
303C4×C73C2×C22⋊Q811yescharacteristic
304Dic73—24no—
305Dic73—82no—
306#20675—731nomaximal, Sylow
307C2×C73—21no—
308C2×C73—21no—
309C2×C73—21no—
310C2×C73—21no—
311C2×C73—21no—
312C2×C73—21no—
313C2×C73—21no—
314C2×C73C2×#38011yescharacteristic
315D73—44no—
316C2×#568—731no—
317C2×#430—731no—
318#2911—731no—
319C2×#421—731no—
320C2×#421—731no—
321#1814—738no—
322C2×#344—731no—
323C2×#344D7311yescharacteristic, complemented
324C73#2067511yescharacteristic, complemented, Sylow
325C22×#41—731no—
326#568—734no—
327#568—734no—
328#568—1462no—
329#568—1462no—
330C2×#131—734no—
331C2×#131—1462no—
332C22×M16—731no—
333C22×M16—731no—
334C22×M16—1462no—
335C22×M16C2×D7311yescharacteristic
336C22×M16C2×D7311yescharacteristic
337C2×#117—731no—
338C2×#117C2×D7311yescharacteristic
339#430—1462no—
340#430—1462no—
341C2×#108—734no—
342#428—1462no—
343#428—1462no—
344#427—734no—
345#421—734no—
346#421—734no—
347#421—1462no—
348#421—1462no—
349C2×#104—1462no—
350C2×#104—1462no—
351#344—734no—
352#344C2×D7314yescomplemented
353C2×#41—732no—
354C2×#41—732no—
355C2×#41—732no—
356C2×#41—732no—
357C2×#41—732no—
358C2×#41—732no—
359C2×#41—1461no—
360C2×#41—1461no—
361C2×#41—1461no—
362C2×#41—1461no—
363C2×#41—1461no—
364C2×#41—1461no—
365C22×Q8—731no—
366C22×D4—731no—
367C22×D4—1461no—
368C23×C4—1461no—
369C23×C4C22×D7311yescharacteristic
370#131—7316no—
371#131—1468no—
372#131—1468no—
373#131—1468no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—732no—
383C2×M16—732no—
384C2×M16—732no—
385C2×M16—732no—
386C2×M16—732no—
387C2×M16—732no—
388C2×M16—732no—
389C2×M16—1464no—
390C2×M16—1461no—
391C2×M16—1461no—
392C2×M16—1461no—
393C2×M16—1461no—
394C2×M16—1468no—
395C2×M16—1468no—
396C2×M16—1461no—
397C2×M16C4×D7312yes—
398C2×M16C4×D7312yes—
399C2×M16C22×D7312yes—
400C2×M16C22×D7312yes—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—732no—
404C22×C8—1464no—
405C22×C8—1461no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—732no—
410#117—1461no—
411#117—1461no—
412#117—1461no—
413#117C22×D7312yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—1461no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1461no—
418C2×C42—21no—
419C2×C42—1461no—
420#108—1468no—
421#107—1464no—
422#106—1464no—
423#104—1468no—
424#104—1468no—
425C24—1461no—
426C24#1192402811yescharacteristic
427#41—734no—
428#41—734no—
429#41—734no—
430#41—734no—
431#41—1462no—
432#41—1462no—
433#41—1462no—
434#41—1462no—
435#41—1462no—
436#41—1462no—
437#41—1462no—
438#41—1462no—
439#41—1462no—
440#41—1462no—
441#41—1462no—
442#41—1462no—
443C2×Q8—732no—
444C2×Q8—732no—
445C2×Q8—732no—
446C2×Q8—1461no—
447C2×Q8—1461no—
448C2×Q8—1461no—
449C2×D4—732no—
450C2×D4—732no—
451C2×D4—732no—
452C2×D4—1462no—
453C2×D4—1462no—
454C2×D4—1462no—
455C2×D4—1462no—
456C2×D4—1462no—
457C2×D4—1462no—
458C2×D4—1461no—
459C2×D4—1461no—
460C2×D4—1461no—
461C22×C4—41no—
462C22×C4—2921no—
463C22×C4—1461no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4—1462no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4C2×C4×D7311yescharacteristic
471C22×C4C2×C4×D7311yescharacteristic
472C22×C4D4×D7311yescharacteristic
473C22×C4D4×D7311yescharacteristic
474C22×C4D4×D7311yescharacteristic
475C22×C4D4×D7311yescharacteristic
476C22×C4D4×D7311yescharacteristic
477C22×C4D4×D7311yescharacteristic
478C22×C4Q8×D7311yescharacteristic
479C22×C4Q8×D7311yescharacteristic
480C22×C4#1192402811yescharacteristic
481C22×C4#1192402811yescharacteristic
482C22×C4#1192402811yescharacteristic
483C22×C4C23×D7311yescharacteristic
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—41no—
490M16—41no—
491M16—2921no—
492M16—2921no—
493M16—734no—
494M16—734no—
495M16—734no—
496M16—734no—
497M16—14616no—
498M16—1462no—
499M16—1462no—
500M16C2×C4×D7314yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—2921no—
508C2×C8—2921no—
509C2×C8—734no—
510C2×C8—734no—
511C2×C8—734no—
512C2×C8—14616no—
513C2×C8—1462no—
514C4⋊C4—22no—
515C4⋊C4—41no—
516C4⋊C4—2921no—
517C4⋊C4—1462no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—2921no—
521C22⋊C4—1462no—
522C42—22no—
523C42—41no—
524C42—2921no—
525C42—1462no—
526C23—81no—
527C23—5842no—
528C23—1462no—
529C23—1462no—
530C23—1462no—
531C23#1455654811yescharacteristic
532C23#1455654811yescharacteristic
533C23#1455656411yescharacteristic
534C23#1455656411yescharacteristic
535C23#1455656911yescharacteristic
536C23#1455656911yescharacteristic
537C23C2×#1192402811yescharacteristic
538Q8—734no—
539Q8—1462no—
540Q8—1462no—
541Q8—1462no—
542D4—734no—
543D4—1464no—
544D4—1464no—
545D4—1464no—
546D4—1464no—
547D4—1462no—
548D4—1462no—
549D4—1462no—
550C2×C4—42no—
551C2×C4—82no—
552C2×C4—2922no—
553C2×C4—5842no—
554C2×C4—1462no—
555C2×C4—1462no—
556C2×C4—1462no—
557C2×C4—1464no—
558C2×C4—1464no—
559C2×C4—1464no—
560C2×C4—1464no—
561C2×C4C22⋊C4×D7311yescharacteristic
562C2×C4C22⋊C4×D7311yescharacteristic
563C2×C4C22⋊C4×D7311yescharacteristic
564C2×C4C22⋊C4×D7311yescharacteristic
565C2×C4C4⋊C4×D7311yescharacteristic
566C2×C4C4⋊C4×D7311yescharacteristic
567C2×C4C4⋊C4×D7311yescharacteristic
568C2×C4C4⋊C4×D7311yescharacteristic
569C2×C4#1455654811yescharacteristic
570C2×C4#1455654811yescharacteristic
571C2×C4#1455656411yescharacteristic
572C2×C4#1455656411yescharacteristic
573C2×C4#1455656411yescharacteristic
574C2×C4#1455656411yescharacteristic
575C2×C4#1455656411yescharacteristic
576C2×C4#1455656411yescharacteristic
577C2×C4#1455656911yescharacteristic
578C2×C4#1455656911yescharacteristic
579C2×C4#1455656911yescharacteristic
580C2×C4#1455656911yescharacteristic
581C2×C4#1455656911yescharacteristic
582C2×C4#1455656911yescharacteristic
583C2×C4C22×C4×D7311yescharacteristic
584C2×C4C2×D4×D7311yescharacteristic
585C2×C4C2×D4×D7311yescharacteristic
586C2×C4C2×D4×D7311yescharacteristic
587C2×C4C2×Q8×D7311yescharacteristic
588C2×C4C2×#1192402811yescharacteristic
589C8—24no—
590C8—42no—
591C8—2922no—
592C8—738no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—2924no—
601C22—5842no—
602C22—5842no—
603C22—1464no—
604C22#1798844611yescharacteristic
605C22#1798844611yescharacteristic
606C22#1798844611yescharacteristic
607C22#1798844611yescharacteristic
608C22C2×#1455654811yescharacteristic
609C22C2×#1455656411yescharacteristic
610C22C2×#1455656911yescharacteristic
611C4—82no—
612C4—5842no—
613C4—1464no—
614C4#1798844611yescharacteristic
615C4#1798844611yescharacteristic
616C4#1798844611yescharacteristic
617C4#1798844611yescharacteristic
618C4C2×C22⋊C4×D7311yescharacteristic
619C4C2×C4⋊C4×D7311yescharacteristic
620C4C2×#1455656411yescharacteristic
621C4C2×#1455656911yescharacteristic
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—21no—
629C2—2924no—
630C2C2×#1798844611yescharacteristic
subgroupG/H
centerC4C2×#14556564
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#344×C73C2
socleC2×C73C2×#380
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenterC2×#344D73
hypocenterC73#20675
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#17988635C2semidirect
3. #22618520C2semidirect
6. #22609984C2semidirect
7. C2×#17988359C2semidirect
8. C2×#344×C73C2semidirect
12. #17989353C4semidirect
13. #17989353C4semidirect
22. C2×#14556526C22semidirect
25. #17988623C22semidirect
32. #17988359C22semidirect
36. #344×C73C22semidirect
54. #14556599C2×C4semidirect
323. C2×#344D73semidirect
324. C73#20675semidirect
352. #344C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179893532
C2×#179886352
#226185202
C2×#179886052
C2×#179886032
#226099842
C2×#179883592
C2×#344×C732
#2067573